Solve
∣
2
x
−
3
∣
=
1
∣2x−3∣=1

To solve the equation \( |2x - 3| = 1 \), we need to consider the two possible cases for an absolute value equation. 

### Case 1: \( 2x - 3 = 1 \)

1. Solve for \(x\):
   \[
   2x - 3 = 1
   \]
   Add 3 to both sides:
   \[
   2x = 4
   \]
   Divide by 2:
   \[
   x = 2
   \]

### Case 2: \( 2x - 3 = -1 \)

1. Solve for \(x\):
   \[
   2x - 3 = -1
   \]
   Add 3 to both sides:
   \[
   2x = 2
   \]
   Divide by 2:
   \[
   x = 1
   \]

### Final Solution:
The solutions are \( x = 2 \) and \( x = 1 \).

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How do you solve an absolute value inequality?
2. What are the properties of absolute value functions?
3. How would the solution change if the equation was \( |2x - 3| = 5 \)?
4. Can absolute value equations have no solutions?
5. How do you graph an absolute value equation?

**Tip**: When solving absolute value equations, always consider both the positive and negative cases!

Learn how to solve the absolute value equation |2x - 3| = 1 with a detailed step-by-step breakdown. This guide covers algebraic concepts like absolute value and how to consider both positive and negative cases. Ideal for students in Grades 7-9.

Math Problem Statement

Solve ∣ 2 x − 3 ∣

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